The city of Tripoli in western Libya was home to a thriving Jewish community until about the early 1970s, when various political and social factors pushed the remaining members of the community to emigrate, completing the process of Libya losing its Jewish communities begun several decades earlier. Now, Jewish Libyan communities are still thriving, but in the diaspora, principally in Italy and Israel.
Since many members of the community still speak their Arabic dialect at home, it is still possible to do linguistic fieldwork and describe Jewish Libyan dialects. However, so far no dialects except that of Tripoli have received attention.
The most important study of Jewish Libyan Arabic is The Arabic dialect of the Jews of Tripoli (Libya) by Sumikazu Yoda (Harrassowitz, 2005). Yoda’s work is the only detailed description of a Libyan Jewish dialect that exists. Although written for a linguistic audience, it also contains the transcription and translation of a fairy tale (“The Sultan and the three sisters”) as well as a glossary, both of which are useful for the non-linguist reader who might want to get an idea of what the Jewish dialect of Tripoli was like.
Fortunately, Yoda also made his recording of that fairy tale available online, which you can listen at this link. It was narrated by Mere Hajjaj Liluf (میري حجاج ليلوف), who was born in Tripoli in 1925, and recorded in Israel in the 1990s.
For those who speak Libyan Arabic, the main differences to note are that t ت becomes ch چ, h ه disappears, and q ق is pronounced q and not g. So for example انتا is pronounced انچا and تعالى sounds like چَعْلا che3la. Or instead of hada هدا you hear ada ادا. I’d be interested to know how much is understandable!